So to clarify, are you referring to the quests which give you a choice of e.g. Harmony, or Purity & Supremacy? Those quests (such as 'Familiar Exotics') don't actually give you affinity points - the quest is just about deciding which path to take. So if you select the Harmony option, for example, the next step of the quest will go in one direction, whereas if you select Purity & Supremacy, it'll go in another.
Could you please identify the specific quests which are not giving you affinity points?
And just to clarify again, have you researched any techs which should grant you affinity points?